Fig. 1. Typical Raman spectra of MoS2 and WS2 scattering from in-plane (ei⊥c axis). (a) Typical Raman-scattering spectrum of MoS2 excited by a 633 nm laser, and a large number of LA(M)-related RS modes are excited. All recoded modes in MoS2 Raman spectroscopy are identified as 179 [A1g(M)+LA(M)], 383 [E2g1(Γ)], 409 [A1g(Γ)], 421 [B2g2+E1u2(Γ−A)], 454 [2LA(M)], 465 [A2u(Γ)], 529 [E1g(M)+LA(M)], 572 [2E1g(Γ)], 600 [E2g1(M)+LA(M)], 644 [A1g(M)+LA(M)], 767 (unknown), 785 (unknown), and 824 (unknown) cm−1 [14,16]. (b) Typical Raman-scattering spectrum of WS2 excited by a 532 nm laser, and the recoded modes are identified as LA(M) at 175  cm−1, E2g1(M)−LA(M) at 195  cm−1, A1g(M)−LA(M) at 233  cm−1, 2LA(M)−2E2g2(M) at 298  cm−1, E1g(M) at 323  cm−1, 2LA(M) at 351  cm−1, A1g(Γ) at 421  cm−1, E2g1(M)+LA(M) at 523  cm−1, A1g(M)+LA(M) at 585  cm−1, and 4LA(M) at 701  cm−1 [9].

Fig. 2. Normalized optical absorption coefficients of the cross section (ki∥a axis) in (a) MoS2 and (b) WS2 calculated via first principles, where ordinate θ is the angle between the incident light polarized vector ei and the c axis of the crystals. The absorption coefficients of the in-plane area (ki∥c axis) in (c) MoS2 and (d) WS2, where the ordinate φ represents the angle between the incident light ei and the c axis.

Fig. 3. Improved Raman spectra of (a) MoS2 and (b) WS2 scattering from out-of-plane polarization (ei∥c axis). Compared to Fig. 1, the RS modes here are fully suppressed and the high SNR of the OP mode is highlighted.

Fig. 4. The cross-sectional angle-dependent polarized (CAP) Raman spectra of (a) MoS2 and (b) WS2, where the ordinate θ is defined as the angle between the incident light polarization ei and the c axis, and the in-plane angle-dependent polarized (IAP) Raman spectra of (c) MoS2 and (d) WS2, where the ordinate φ is defined as the angle between the incident light polarization ei and the a axis.

Fig. 5. Raman intensities of OP and RS modes extracted from Figs. 4(a) and 4(b) via Lorentzian fitting. (a) and (b) display angle-dependent intensities of A1g OP modes in MoS2 and WS2, respectively, and reveal a similar changing rule in MoS2 and WS2. The red line gives the corresponding fitting results based on the Raman selection rule, i.e., Eq. (1). (c) and (d) show the angle-dependent intensities of resonant scattering modes in layered MoS2 and WS2, respectively. All modes appear with the same θ angle dependence: when θ=(n+1/2)π, the scattering intensity reaches the highest value; while θ=nπ, the value approximates to zero.